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This paper proposes a dynamic model for the spot foreign exchange rate which is governed by a standard Brownian motion and a stationary compound Poisson process in the domestic-real world. Using the tool of the Esscher transform, we explore two suitable parameters for the amplitude and the intensity of the jump process and redefine the dynamic process of the spot foreign exchange rate under the domestic risk-neutral measure. Based on the above work, we obtain two types of the quanto option pricing formulas. At last, we utilize the real market data of the stock "Aluminum Corporation of China Limited" and the foreign exchange rate of USD/CNY to obtain the value of the quanto option taken the constant K1 as the strike price in the domestic currency. Furthermore, we investigate the implied volatility of the quanto option. [ABSTRACT FROM AUTHOR]

This paper addresses the cooperative adaptive consensus tracking for a group of multiple nonholonomic mobile robots, where the nonholonomic robot model is assumed to be a canonical vehicle having two actuated wheels and one passive wheel. By integrating a kinematic controller and a torque controller for the nonholonomic robotic system, a cooperative adaptive consensus tracking strategy is developed for the uncertain dynamic models using Lyapunov-like analysis in combination with backstepping approach and sliding mode technique. A key feature of the developed adaptive consensus tracking algorithm is the introduction of a directed network topology into the control constraints based on algebraic graph theory to characterise the communication interaction among robots, which plays an important role in realising the cooperative consensus tracking with respect to a specific common reference trajectory. Furthermore, a novel framework is proposed for developing a unified methodology for the convergence analysis of the closed-loop control systems, which can fully ensure the desired adaptive consensus tracking for multiple nonholonomic mobile robots. Subsequently, illustrative examples and numerical simulations are provided to demonstrate and visualise the theoretical results. [ABSTRACT FROM AUTHOR]

In the real world, we introduce a dynamic model about the risky asset which is governed by Brownian motion, stationary compound Poisson process and its compensation process. By choosing Esscher transform parameters, we obtain a risk-neural measure Q under which the discounted value of the risky underlying asset is a martingale. Then, we give the pricing formulas of Exchange option by change of numeraire. At last, we analyze the option pricing formula and provide numerical illustrations by introducing BBY stock and SBUX stock. [ABSTRACT FROM AUTHOR]

In this paper, we price the vulnerable option under the assumption that both underlying and counterparty asset price follow correlated jump diffusion processes. By the two-dimensional Itô-Doeblin formula, we initially derive a partial integro-differential equation (PIDE) satisfied by the price of the vulnerable option with flexible jumps. Then, the double Mellin transform converts the PIDE into an ordinary differential equation (ODE), which possesses an explicit solution. Further, the inverse Mellin transform of the explicit solution to the ODE turns out to be a rigorous solution to the PIDE for vulnerable option. Finally, by carrying out some numerical experiments, we demonstrate that the PIDE's solution produces price with a convincing degree of precision. [ABSTRACT FROM AUTHOR]

In this paper we give direct, inverse, and equivalence approximation theorems with unified Ditzian-Totik modulus [image omitted] (0 ≤ λ ≤ 1) for Meyer-Konig and Zeller operators. [ABSTRACT FROM AUTHOR]

Recently some classical operator quasi-interploants were introduced to obtain much faster convergence. P. Mache and D. H. Mache gave Bernstein quasi-interpolants and obtained approximation equivalence theorem with . In this article we extend above result with modulus which unified classical modulus and Ditzian-Totik modulus. [ABSTRACT FROM AUTHOR]